Structural role of counterions adsorbed on self-assembled peptide nanotubes

Among noncovalent forces, electrostatic ones are the strongest and possess a rather long-range action. For these reasons, charges and counterions play a prominent role in self-assembly processes in water and therefore in many biological systems. However, the complexity of the biological media often hinders a detailed understanding of all the electrostatic-related events. In this context, we have studied the role of charges and counterions in the self-assembly of lanreotide, a cationic octapeptide. This peptide spontaneously forms monodisperse nanotubes (NTs) above a critical concentration when solubilized in pure water. Free from any screening buffer, we assessed the interactions between the different peptide oligomers and counterions in solutions, above and below the critical assembly concentration. Our results provide explanations for the selection of a dimeric building block instead of a monomeric one. Indeed, the apparent charge of the dimers is lower than that of the monomers because of strong chemisorption. This phenomenon has two consequences: (i) the dimer-dimer interaction is less repulsive than the monomer-monomer one and (ii) the lowered charge of the dimeric building block weakens the electrostatic repulsion from the positively charged NT walls. Moreover, additional counterion condensation (physisorption) occurs on the NT wall. We furthermore show that the counterions interacting with the NTs play a structural role as they tune the NTs diameter. We demonstrate by a simple model that counterions adsorption sites located on the inner face of the NT walls are responsible for this size control.     

Anomalously suppressed localization in the two-channel Anderson model

We study numerically the localization properties of a two-channel quasi-one-dimensional Anderson model with uncorrelated diagonal disorder within the nearest-neighbor tight-binding approximation. We calculate and analyze the disorder-averaged transmittance and the Lyapunov exponent. We find that the localization of the entire system is enhanced by increasing the interchain hopping strength t?. From the numerical investigation of the energy dependence of the Lyapunov exponent for many different interchain hopping strengths, we find that apart from the band center anomaly, which usually occurs in strictly one-dimensional disordered systems, additional anomalies appear at special spectral points. They are found to be associated with the interchain hopping strength and occur at E = ± t?/2 and ± t?. We find that the anomalies at E = ± t? are associated with the π-coupling occurring within one energy band and those at E = ± t?/2 are associated with the π-coupling occurring between two different energy bands. Despite having a similar origin, these two anomalies have distinct characteristics in their dependence on the strength of disorder. We also show that for a suitable range of parameter values, effectively delocalized states are observed in finite-size systems.     

A new family of convex weakly compact valued random variables in Banach space and applications to laws of large numbers

We consider a new family of convex weakly compact valued integrable random sets which is called an adapted array of convex weakly compact valued integrable random variables of type p (1?p?2). By this concept, more general laws of large numbers will be established. Some illustrative examples are provided.     

Existence of traveling waves in compressible Euler equations with viscosity and capillarity

Given any Lax shock of the compressible Euler dynamics equations, we show that there exists the corresponding traveling wave of the system when viscosity and capillarity are suitably added. For a traveling wave corresponding to a given Lax shock, the governing viscous–capillary system is reduced to a system of two differential equations of first-order, which admits an asymptotically stable equilibrium point and a saddle point. We then develop the method of estimating attraction domain of the asymptotically stable equilibrium point for the compressible Euler equations and show that the saddle point in fact lies on the boundary of this set. Then, we establish a saddle-to-stable connection by pointing out that there is a stable trajectory leaving the saddle point and entering the attraction domain of the asymptotically stable equilibrium point. This gives us a traveling wave of the viscous–capillary compressible Euler equations.